Pre-Algebra Examples

$16 (n + 2) = 4 (8 + 4 n)$

Step 1

Simplify $16 (n + 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 16 (n + 2) = 4 (8 + 4 n)$

Step 1.2

Simplify by adding zeros.

$16 (n + 2) = 4 (8 + 4 n)$

Step 1.3

Apply the distributive property.

$16 n + 16 \cdot 2 = 4 (8 + 4 n)$

Step 1.4

Multiply $16$ by $2$ .

$16 n + 32 = 4 (8 + 4 n)$

Step 2

Simplify $4 (8 + 4 n)$ .

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Step 2.1

Apply the distributive property.

$16 n + 32 = 4 \cdot 8 + 4 (4 n)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $4$ by $8$ .

$16 n + 32 = 32 + 4 (4 n)$

Step 2.2.2

Multiply $4$ by $4$ .

$16 n + 32 = 32 + 16 n$

Step 3

Move all terms containing $n$ to the left side of the equation.

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Step 3.1

Subtract $16 n$ from both sides of the equation.

$16 n + 32 - 16 n = 32$

Step 3.2

Combine the opposite terms in $16 n + 32 - 16 n$ .

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Step 3.2.1

Subtract $16 n$ from $16 n$ .

$0 + 32 = 32$

Step 3.2.2

Add $0$ and $32$ .

$32 = 32$

Step 4

Since $32 = 32$ , the equation will always be true for any value of $n$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$